A common operation in various NMR measurements is the inversion of the nuclear magnetization. This is commonly achieved by applying a 180.degree. pulse at the RF resonant frequency. A high degree of homogeneity is not also obtained in either or both of the polarizing and RF fields and the frequency range over which such inversion is desired may be substantial. The application of NMR to spatial imaging is one example. Another is the case where it is desired to obtain heteronuclear decoupling over a relatively wide frequency interval.
Adiabatic fast passage is probably the most effective method for inverting nuclear spins over a wide frequency band. It also has the valuable property that the RF level is not critical, provided that it satisfies the adiabatic condition: EQU .vertline.d.theta./dt.vertline.&gt;&gt;.omega..sub.eff Equ. 1
where .omega..sub.eff =.gamma.B.sub.eff is the effective field expressed in angular frequency units through the gyromagnetic ratio .gamma., given by the resultant of the applied RF field .omega..sub.1 =.gamma.B.sub.1 and the resonance offset .DELTA..omega.=.gamma..DELTA.B, and where .theta. is the inclination of B.sub.eff with respect to the +x axis. This also implies that spatial inhomogeneities of B.sub.1 or B.sub.0 are not important in this application.
The adiabatic condition is most critical when the frequency sweep is near resonance (B.sub.eff .apprxeq.B.sub.1) and is more easily satisfied at more appreciable offsets where B.sub.eff is large. It is usual to quantify an adiabaticity factor EQU Q=.omega..sub.eff /.vertline.d.theta./dt.vertline. Equ. 2
which should be large compared with unity. A factor of 5 is typical. This may be expressed as EQU Q=(A+.DELTA..omega..sup.2).sup.3/2 /{A d.DELTA..omega./dt-.DELTA..omega.dA/dt} Equ. 3
It is well known that an adiabatic sweep may be implemented either by sweeping the frequency (d.DELTA..omega./dt) or by sweeping the RF amplitude (dA/dt), or both.
A second requirement for good spin inversion is that the effective field B.sub.eff should start on the +z axis and end on the -z axis. Thus a simple constant amplitude linear frequency sweep is unsuitable, because a finite offset .DELTA..omega. remains at the extremities of the sweep, leaving B.sub.eff inclined with respect to the z axis. A symmetrical amplitude profile that goes asymptotically to zero is therefore indicated.
In the prior art, adiabatic fast passage was known to provide magnetic inversion which is relatively insensitive to inhomogeneity of either the RF or polarization field distribution. A frequency sweep is applied having some selected analytic time dependence. In the prior art Baum, Tycko and Pines have proposed a time dependence of the form tan (.beta.t)), or sech(.beta.t) as taught by Silver, Joseph and Hoult. It is shown in the present work that the inversion pulse of the present invention permits inversion over a comparable bandwidth at the same adiabticity factor at lower RF amplitudes. This has practical consequences in lower required power ratings of components of RF probes for example.